Talk:SkyWings/@comment-27191596-20160131205400
We needed to create a math problem to demonstrate our learning in math this semester. My problem: This semester, a kind of problem I have had trouble on is linear programing. I will proceed to write a problem that shows I am better than that now. The SkyWings are debating how many SeaWings and IceWings to take prisoner and force to fight in the arena, instead of killing them outright. SkyWing prisoners of war usually last 1 month before dying. They also take food to feed. An average SeaWing eats 100 pounds of food in a month. An average IceWing eat 110 pounds of food each month. The SkyWings have 6,000 lbs of food for prisoners this month.They also had a great general recently killed by SeaWings. The SkyWings are especially angry at them and want at least 15 more SeaWing prisoners than IceWings. And SeaWings last an average of 2.5 battles. IceWings last an average of 3.5 matches. The SkyWings want at least 150 battles.They also want the greatest number of IceWing prisoners possible. Determine what numbers of IceWings and SeaWings satisfies all conditions and has the greatest number of IceWings. 1)Define variables x= #IceWing prisoners y= #SeaWing prisoners My reasoning is that since the question is asking how many SeaWings and how many SkyWings, those should be my variables. 2)Write equations a.lbs of food per IceWing + # lbs of food per SeaWing < total lbs of food 110x+100y < 6,000 /100 1 1/10 x+y < 60 -1 1/10x y < 60-1 1/10 x (shown in red) b. # SeaWings > 15 + # Icewings y > 15+x (shown in blue) c. # IceWing matches + # SeaWing matches > total matches 3 ½ x +2 ½ y > 150 /2 ½ 1 ⅖ x +y > 60 -1 ⅖ x y > 60-1 ⅖ x (shown in green) My reasoning for the first equation is that, since SeaWings are y, subtract 110 x from each side and then divide each side by 100. For the second equation, the number of IceWings + 15 is less than or equal to the number of SeaWings. For the final equation, the number of battles divided by the SeaWing survival rate - (the number of battles a typical Icewing fights / the number of battles an average SeaWing fights) < the number of SeaWings to meet both conditions. 3) Graph, find intersections. i. Hit Y= ii. Enter equations iii. Set a realistic window iv.Push Graph v. Hit 2ND and Trace vi.Hit 5 vii. Hit ENTER twice viii.Record given intersection ix. Repeat steps v and vi x. Hit ENTER once and maneuver pointer to a different line, then press ENTER xi.Record. xii.Repeat steps ix through xi, but do not press Enter beforehand on step x xiii.Repeat step xi (19,34) (0,60) (21,36) My reasoning is that this technique helps me solve simultaneous equations and gives me the solutions for any pair, in the _____ of the third. It helps me see the special relationship between all the equations. 4)Find point that has greatest # of IceWings (21,36) The SkyWings’ final condition is that they would like the greatest number of IceWing prisoners possible. This point represents that condition. 5)Write summary Since the variable x represents the number of IceWings and the variable y represents the number of SeaWings, the solutions to this represent the possible combinations of IceWings and SeaWings that the SkyWings could take prisoner. This answer means that the SkyWings should take 21 IceWings and 36 SeaWings prisoner. IceWings, SkyWings, and SeaWings belong to author Tui T. Sutherland. All “facts”, however, belong to me.